IMO The Google IME is the best wat to go about it. As far as typing goes all IMEs are about the same.
a,i,u,e,o,ka,ki,ku,ke,ko, etc

The only thing is for typing the smaller characters (mainly in katakana) you type “x” first (if the don’t come up automatically):
ァ:xa
ィ:xi
ゥ:xu
ェ:xe
ォ:xo

し is either shi or si
ち　is either chi or ti
ぢ is either dzi or di
つ is either tsu or tu
づ　is either dzu or du

(There is a lesson on this early on in textfugu, isn’t there?)

Alternatively, you can also use “l” to type smaller characters (l for “little”? haha).

Or rather, you can in the default Windows IME. I’m assuming Google’s will too.

Yeah, I use L too. There’s a few other fun combinations you can discover through random experimentation too – for example, “qi” outputs くぃ. =)

As an added tip, if anyone’s using the Microsoft IME and you find a word containing the dreaded づ, just type ‘du’ and it should appear. =)